In the 19th century, gradualist assumptions were
behind the thinking of most catastrophists as well as
uniformitarians--and, in another field of study, even the Darwinians.
To them, life--and earth--consists mostly of a series of small
sometimes imperceptible moves over many millions of years. At first
glance, to gradualists, evolution, not revolution, seems to have
been, and to be, the norm.
Those gradualist assumptions continue into the 20th
century, with certain exceptions for those in the natural scienes who
believe in what they call 'punctuated equilibrium'--gradualism as
usual interrupted by presumably unusual catastrophes.
A traditional gradualist assumption shared with
uniformitarians has been that natural laws are immutable: now equals
then and then equals now. The past and the present (and presumably
the future) are as one.
But note: you can't logically believe in no fundamental
change and some fundamental change (whether evolutionary or
revolutionary) at the same time.
One gradualist assumption is that global catastrophes
are not only rare but irregular and inconsistent. They are assumed to
have no underlying pattern of recurrence and no consistent mechanism
to create that recurrence. A possible exception would be certain
extraterrestial mechanisms such as comets which appear, strangely
enough, to be psychologically easier to accept than earth-bound
mechanisms of global catastrophe.
Note: If terrestrial mechanisms can't be conceived of
as revolutionary in nature, must global catastrophes that have
occured always be assumed to have been totally random or can they be
thought of as in some sense evolutionary--or some combination of the
Gradualist thinking, of course, is re-enforced by the
results of radiometric dating methods which, by creating
millions-of-years time-lines, tilt the mind away from thoughts of
suddenness towards the infinitesimally slow. One could argue, of
course, that's what objective evidence shows must be done.
To most people, the theory of plate tectonics is the
prime example of gradualist thinking in current geology.